Getz, Wayne M. “Polycondensation and peptide chain-length distribution under prebiotic conditions.” Biosystems 24, no. 3 (1990): 177-182.
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An open-ended system of differential equations is formulated for the number of polymers of length n , n = 1,2,…, under the assumption that all monomers are kinetically equivalent. Although this assumption does not hold in real systems, solutions to the model could provide insights into the processes of polycondensation including polymerizing proteins and polynucleotides. In this paper the equilibrium solution to the system is derived analytically and is used to estimate the concentration of monomers required to obtain a fixed proportion of polymers longer than a given length. Simulation results are also presented to indicate the effects that autocatalytic interactions may have on the dynamics of polycondensation. The results suggest that relatively long-chained peptides (one to several hundred units long) could well have been synthesized under non-template or prebiotic conditions.